Are there Python packages for random search hyper-parameter optimisation?
Welcome to AI.SE Enes.

I think by random search, you are referring to so-called "black-box optimization". Random search is sometimes used as a name for this, but BBO is a more common name, and might be easier to search for.

There are many BBO techniques. 'random search' is usually used to refer to a hill-climbing algorithm where you start at a random location, sample from 'adjacent' points in the input space, and then pick the best one to move to.

Scikit-optimize is fairly easy to use package, and implements some of the most reasonable algorithms (gaussian process is particularly strong on most problems). The package's website includes many good examples showing how to use the methods the package provides.

If you're not happy with those methods, then you are likely entering 'unsupported land'. There are lots of more complex, esoteric, methods, but I don't believe they are well consolidated into a single package (or even a single language). There's a nice collection on the Sahindis lab's website, but those are in a mixture of C and Fortran. There are also a huge number of algorithms submitted to recurring competitions, like this one at GECCO each year, but the implementations of these algorithms may not be available at all, or might be available only through the websites of their respective authors.